Question 847916
<pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
log base6(12) + log base 6(3) = (2/3)x
log base6(36)= (2/3)x  
{{{(3/2)log(6,36) = x}}}
{{{ log(6,36^(3/2)) = x}}}   *[tex \large\ \ nlog_bx = log_b(x^n) ]
{{{ log(6,(6^2)^(3/2)) = x}}}        {{{(a^p)^q = a^(p*q)}}}
{{{ log(6,6^3)= x}}}    *[tex \large\ \ log_b(x) \ = \ y \ \ \Rightarrow\ \ b^y = x]
         6^x = 6^3
           x = 3

*[tex \large\ \ log_b(x) \ = \ y \ \ \Rightarrow\ \ b^y = x]
*[tex \large\ \ nlog_bx = log_b(x^n) ]
*[tex \large\ \ log_bx + log_by = log_b(xy) ]
*[tex \large\ \ log_bx - log_by = log_b(x/y) ]
*[tex \large\ \ log_b1 = 0]
*[tex \large\ \ log_bb = 1]
{{{a^0 = 1}}}
{{{(a^p)^q = a^(p*q)}}}
{{{root(a,p)*root(a,q) = root(a,p*q)}}}  
{{{x^m/x^n=x^(m-n)}}}
{{{( x^m )( x^n ) = x^( m + n )}}}
{{{root(n, (x/y)) = root(n,x)/root(n,y)}}}
{{{(xy)^n = x^n*y^n}}}
{{{x^(1/n) = root(n,x)}}}   , {{{x^(m/n) = (root(n,x))^m}}}